In my opinion, four items matter most of all.
#1 - You being able to control light in the room.
That's it, period! You don't watch a movie in the theater with the lights turned halfway up for a reason. It is because your screen is white, and when you shine a light on it, the screen becomes more and more visibly white. The ONLY way to achieve black is through absence of light, which you can only generate with front projection by starting with a 100% dark room. You can have so-so results, at best, without light control.
2. Color
Getting good color is missed in many projectors, most often business class projectors. Those cheap projectors at Staples are not what you want in your family room projecting onto the wall. You want a projector that is designed to give you flesh tones that aren't of the more common business class shade of martian.
3. Motion handling - This is another huge deficiency in the business class projector department. The projector really should handle incoming video and be able to deliver it to the screen clean and smooth. Any serious motion artifacts and details that are lost due to the projector having poor processing is a big loss to the overall quality. I'm kind of lumping video scaling and image processing into this group.
4. Black levels/shadow details/contrast - This goes back to #1 on the list. But #1 is the key. A projector with a rated contrast ratio of 5,000:1 has a drop of contrast to 500:1 with the light from a SINGLE candle added to the room. But, if you watch after dark, then those sci-fi movies and all dark scenes in general will carry the full detail that was on the original film. The newest generation of LCD & DLP home theater projectors do an excellent job with black levels and contrast.
As you can see, lumens are not on this list. Specifically this is because if you actually look at about 20 or so home theater projectors in price ranges from $1,000 to about $30,000 you will find that they all have one thing in common - They have VERY similar light output levels.
Home theater projectors are calibrated to output correct light levels for home theater. That means, ideal home theater with light control and a screen in the 7-11 foot wide range.
There is a ton of information - hours and hours of reading - along with some forum info over at
www.projectorcentral.com
Go give that a read.